cp's OEIS Frontend

A187859 Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

%I A187859 #10 Apr 26 2018 08:56:39
%S A187859 0,0,216,968,2754,5428,9237,14040,19837,26628,34413,43192,52965,63732,
%T A187859 75493,88248,101997,116740,132477,149208,166933,185652,205365,226072,
%U A187859 247773,270468,294157,318840,344517,371188,398853,427512,457165,487812
%N A187859 Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.
%C A187859 Row 4 of A187857.
%H A187859 R. H. Hardin, <a href="/A187859/b187859.txt">Table of n, a(n) for n = 1..50</a>
%F A187859 Empirical: a(n) = 497*n^2 - 2652*n + 3448 for n>5.
%F A187859 Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F A187859 G.f.: x^3*(216 + 320*x + 498*x^2 - 146*x^3 + 247*x^4 - 141*x^5) / (1 - x)^3.
%F A187859 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A187859 (End)
%e A187859 Some solutions for 4 X 4:
%e A187859 ..0..0..0..0....3..2..4..0....0..0..0..0....0..4..0..0....0..0..0..4
%e A187859 ..0..0..0..0....0..1..0..0....0..4..3..0....0..0..3..0....0..3..2..0
%e A187859 ..4..3..2..0....0..0..0..0....2..1..0..0....1..0..2..0....0..0..0..1
%e A187859 ..0..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%Y A187859 Cf. A187857.
%K A187859 nonn
%O A187859 1,3
%A A187859 _R. H. Hardin_, Mar 14 2011